What was the method Umar ibn al-Khattab and his servant followed in riding the mount alternately during their journey to Jerusalem?

Historians mentioned that Umar ibn al-Khattab, may Allah be pleased with him, took turns with his servant equally on his journey to Jerusalem, without specifying the duration or distance. Umar learned this from the Prophet, peace and blessings be upon him, for the Prophet used to alternate walking with his companions in the Battle of Badr, refusing for them to walk on his behalf, saying: "Neither of you is stronger in walking than me, nor am I in less need of reward than you." The narrations did not specify the duration or distance of this turn-taking.